Continuum Mechanics

  1. Mathematical Foundations
    1. Coordinate Systems
      1. Cartesian Coordinates
        1. Curvilinear Coordinates
          1. Coordinate Transformations
            1. Orthogonal Coordinate Systems
            2. Index Notation and Summation Convention
              1. Einstein Summation Convention
                1. Free and Dummy Indices
                  1. Index Manipulation Rules
                    1. Kronecker Delta
                      1. Permutation Symbol
                      2. Vector Analysis
                        1. Vector Operations
                          1. Dot Product
                            1. Cross Product
                              1. Triple Products
                                1. Vector Identities
                                2. Tensor Algebra
                                  1. Definition of Tensors
                                    1. Tensor Transformation Laws
                                      1. Tensor Order and Rank
                                        1. Scalars
                                          1. Vectors
                                            1. Second-Order Tensors
                                              1. Higher-Order Tensors
                                              2. Tensor Operations
                                                1. Addition and Subtraction
                                                  1. Scalar Multiplication
                                                    1. Tensor Products
                                                      1. Dyadic Product
                                                        1. Contraction
                                                          1. Double Contraction
                                                          2. Trace
                                                            1. Determinant
                                                              1. Transpose
                                                              2. Special Tensors
                                                                1. Identity Tensor
                                                                  1. Zero Tensor
                                                                    1. Symmetric Tensors
                                                                      1. Skew-Symmetric Tensors
                                                                        1. Orthogonal Tensors
                                                                          1. Isotropic Tensors
                                                                        2. Tensor Calculus
                                                                          1. Gradient Operations
                                                                            1. Gradient of Scalar Fields
                                                                              1. Gradient of Vector Fields
                                                                                1. Gradient of Tensor Fields
                                                                                2. Divergence Operations
                                                                                  1. Divergence of Vector Fields
                                                                                    1. Divergence of Tensor Fields
                                                                                    2. Curl of Vector Fields
                                                                                      1. Laplacian Operator
                                                                                        1. Material Derivative
                                                                                          1. Integral Theorems
                                                                                            1. Divergence Theorem
                                                                                              1. Stokes' Theorem
                                                                                                1. Transport Theorems
                                                                                              2. Eigenvalue Problems
                                                                                                1. Principal Values
                                                                                                  1. Principal Directions
                                                                                                    1. Spectral Decomposition
                                                                                                      1. Diagonalization
                                                                                                        1. Invariants

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                                                                                                      1. Introduction to Continuum Mechanics

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                                                                                                      3. Kinematics of Deformation